Chapter 10 (Sp11)

Chapter 10 (Sp11) - Section 10.1 – The Language of...

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Unformatted text preview: Section 10.1 – The Language of Hypothesis Testing A HYPOTHESIS is a claim or statement about a characteristic of one or more populations. A HYPOTHESIS TEST is a procedure, based on sample evidence and probability, used to test claims about a characteristic of one or more populations. Because we are using sample data to test the claim, we cannot say with 100% certainty that the statement is true; we can only determine if the sample data support the claim or not. Components of a Hypothesis Test: I. State H and H 1 with symbols. ( p , σ μ , ) The NULL HYPOTHESIS (denoted H o ) is a statement that the value of a population parameter ( μ , p , σ ), is equal to some claimed value. During the test, you assume that H o is true until the evidence indicates otherwise. In the conclusion, you will either reject H o or you will not reject H o . H o : μ = # (mean) H o : p = # (proportion) H o : σ = # (standard deviation) The ALTERNATIVE HYPOTHESIS (denoted H 1 or H A ) is a statement that the parameter somehow differs from H o . It is the statement we are trying to find evidence to support. It cannot contain equality, and it must be true if H o is false. H 1 : μ ≠ # H 1 : μ > # H 1 : μ < # (mean) H 1 : p ≠ # H 1 : p > # H 1 : p < # (proportion) H 1 : σ ≠ # H 1 : σ > # H 1 : σ < # (standard deviation) A TWO-TAILED test occurs when H 1 contains a ≠ symbol. You must split α evenly into two tails. A LEFT-TAILED test occurs when H 1 contains a < symbol. All of α goes in the left tail. A RIGHT-TAILED test occurs when H 1 contains a > symbol. All of α goes in the right tail. Examples : Identify H o and H 1 then determine if the test is left tailed, right tailed, or two tailed. a) Salaries among major-league baseball players have a standard deviation that is not $2500. 1 b) The percentage of male voters is less than 40%. c) The mean amount of water in a bathtub is more than 124 gallons. II. Determine the α level. Determine the critical value (Z, t , 2 χ ). (this will come from a table) LEVEL OF SIGNIFICANCE (α) is the probability of making a Type I error. The CRITICAL VALUE is any value that separates the critical region from the values of the test statistic that do not lead to a rejection of H o . The CRITICAL REGION (rejection region) is the set of all values of the test statistic that will cause us to reject H o . For TWO-TAILED test --- You must split α evenly into two tails. For LEFT-TAILED test --- All of α goes in the left tail. For RIGHT-TAILED test --- All of α goes in the right tail. Examples : Find the critical z values: a) Two-tailed test, α = 0.01 b) Right-tailed test, α = 0.05 2 Critical Values (Z) for Hypothesis Testing (classical approach) III. Calculate and state the appropriate test statistic (Z, t , 2 χ ) (calculator) A TEST STATISTIC is a value computed from the sample data that is used to make the decision about whether or not H o is rejected. It illustrates the number of standard deviations that the sample statistic is from the assumed parameter in H...
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Chapter 10 (Sp11) - Section 10.1 – The Language of...

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